Optimization Of Automatic Steering Control

Published Date: 02 Nov 2017

1 Electrical Engineering Dept., Widyagama University. Malang, Indonesia, [email protected]

2 Electrical Engineering Dept., ITS Surabaya, Indonesia, [email protected]

3 Mechanical Engineering Dept., ITS Surabaya, Indonesia, [email protected]

Abstract— This paper presents the simulation of the automatic steering control system on a vehicle model using a Particle Swarm Optimization (PSO) to optimize the parameters of the control system, the Fuzzy Logic and PID control. The two control systems working in a cascade, a sequence used to control the lateral motion and yaw motion errors in vehicle models representing 10 degree of freedom of the vehicle dynamics system. Testing is done through the software in the loop simulation resulting that the Fuzzy Logic and PID controls tuned by the PSO in the automatic steering control of vehicle can well adapt the plant output to desired trajectory. Thus the stability of the lateral motion of the vehicle can always be maintained at the prescribed path.

Keywords— Automatic Steering Control, Fuzzy Logic, PID, PSO

Introduction

As one of the vehicle technology development in the future, a steer-by-wire system is expected to have a reliable performance. It is an automatic steering control of vehicle that does not use a mechanical connection instead using electric motors to determine the direction of the front wheels of vehicles [1]. There are two types of characteristics of the steer-by-wire system used namely semi-automatic and fully-automatic. Semi-automatic steering control system is a vehicle that still uses the steer wheel as a plant input and an electric motor as the plant output to drive the front wheels direction of the vehicle [2], while the fully-automatic is the control system without using the steering wheel so as to determine the direction of the front wheels of vehicles used a programmed trajectory as an input and output plants that remain to use an electric motor [3].

There are a lot of researches that have been developing on a fully-automatic steer-by-wire system, among other researches focused on the input trajectory with look-ahead and look-down systems [4], using GPS technology [5] and a trajectory using the lane guidance [3]. Similarly, some researchers have been developed on the automatic steering control technique involving Artificial Intellegence (AI), among others, Automatic Steering Control of Vehicle based Genetic Fuzzy Controller [6], adaptive fuzzy logic - a neural network model [7]. A fuzzy Logic including techniques is widely applied to the vehicle steering control. However, to obtain the parameters required by a Fuzzy Logic Control (FLC) is reliable is not easy work, since it often deals with the complexity of the optimization problem and needs a large memory in the computing process. A Particle Swarm Optimization (PSO) is an optimization method that offers the fast and accurate optimization for FLC tuning parameters [8,9].

In this paper, a model of fully-automatic steer-by-wire system represented in a simulation of automatic steering control of vehicle using a model with 10 degree of freedom (DOF) consisting of 7-DOF of the vehicle ride model, and 3-DOF of the vehicle handling model [10,11] is developed. The structure of the developed control system consists of two stages in cascade, namely lateral motion control to eliminate unwanted lateral movement and this control output will be used as the setting point of the next control, i.e., yaw motion control as a complement steering control system. The Control System involves the PSO to tune the parameters of FLC in control of lateral motion and tuning parameters Proportional-Integral-Derivative (PID) controller to control of the yaw motion. The expected results of the simulation automatic steering control using the FLC and PID control tuned by the PSO can improve the vehicle dynamic performance, which in turn will be a recommendation to be implemented in hardware in the loop simulations.

This present article consists of the following sections: 1) the introduction and the review of some researches that have been done. 2) the vehicle model with 10-DOF vehicle dynamic. 3) structural model for the simulation of automatic steering control, FLC and PID control tuned by PSO, 4) the results of the simulation and discussion, and 5) conclusion.

Vehicle dynamic model

Based on the concept of vehicle dynamics, the vehicle model is built as a plant of the automatic steering control system using the 10-DOF consisting of the 7-DOF of the vehicle ride model, and 3-DOF of the vehicle handling model.

Vehicle Ride Model

Vehicle Ride Model is represented as a 7-DOF system expressed in mathematical equations consisting of seven equations in the car body with a freedom of movement to heave or bouncing, pitching, rolling and vertical direction for each wheel [10,11] as shown in figure 1.

Bouncing of the car body (Zs) is represented as

(1)

Where the Pitching of the car body ( ) is as follows:

(2)

Rolling of the car body ( ) is expressed as

(3)

Vertical Direction for each wheel is

(4)

(5)

(6)

(7)

Vehicle Handling Model

Vehicle Handling Model is represented as a 3-DOF system, meaning that it has three mathematical equations consisting of the equations of the movement of the car body; lateral and longitudinal as well as yaw motions [12,13] as shown in figure 2. The lateral and longitudinal motions are the movement of vehicles along the x axis and y axis expressed in lateral acceleration (ay) and longitudinal acceleration (ax) so that the lateral and longitudinal motions can be obtained by a double integration of the lateral and longitudinal acceleration.

Lateral and longitudinal acceleration are expressed as follows:

(8)

(9)

An angular movement of the vehicle, which is based on the vertical axis is called a yaw motion z (r) [14] which can be obtained by the integration of and

(10)

Definitions of variables are shown in Table 1.

Based on the above equation, then a full vehicle model is established as the plant of the automatic steering control systems using MATLAB-SIMULINK software, by taking δ as the steering input to the plant (equations 8, 9, 10) and the plant output is expressed in three movement of vehicles, the longitudinal motion (x) in Equation 8, lateral motion (y) in Equation 9 and yaw motion (r) in Equation 10. Yaw motion will affect the moment of inertia around the z-axis (Jz), this will lead to changes in pitch and roll angle at body center of gravity (θ and φ) [11], so it will be more influenced to the entire force in the direction of the z-axis (bounching, pitching, rolling and all vertical direction for each wheel, equations 1-7).

System Control Simulation

An automatic steering control system of the vehicle model that was built in the simulation using the two controllers are cascaded, the first controller is a FLC and the second is the PID control [15], where the control system is needed to set the direction of the front wheels of the vehicle to match the required trajectory (lookup table x - y trajectory) in the form of a double line change and a sine steer trajectory.

The plant output is expressed in the yaw rate and the slip angle, in which the slip angle is a characteristic of the lateral and longitudinal force, so the functions of the control system are as follows: FLC is used to suppress the error among lateral motion (y) associated with the longitudinal motion (x) of the required trajectory, while the PID control is used to accelerate the risetime, minimize errors and to reduce the overshot / undershot among the yaw motion of the setting point which is the output from the FLC. The ideal condition on the output FLC is that if an error has been minimized, it means that the vehicle has no lateral motion (y), meaning that the vehicle also does not have the yaw motion so that the output of the FLC is used as the setting point on the yaw motion controls. To get the optimal control depends on the design from the composition of each parameter control system, and in this paper, the determination of parameter values ​​in both FLC and PID controls is done by tuning the values ​​of these parameters to achieve the optimal value by using the PSO. A block diagram of the control structure used in the automatic steering control simulation is shown in figure 3.

Fuzzy Logic Controller (FLC)

FLC is the primary control on the proposed control structure which is used to minimize the error among input and output of the plant, i.e. lateral motion error. The main structure of the FLC, among others, consists of [16] the following points:

- fuzzification crisp variables, where in this process, there are an error and the delta error which are converted into fuzzy variables using the technique Membership Functions (MF). MF is a function to express the degree of fuzzy membership. The form of MFs used in this paper is a triangular shape (Triangular Function), and each MF on the input (error and error delta) and the output comprise seven triangular MF, and have a term language; Negative Big (NB), Negative Medium (NS ), Negative Small (NK​​), Zero (Z), Positive Small (PK), Positive Medium (PS), Positive Big (PB).

Triangular shape of each MF can be changed based on the width and the center point, depending on the multiplier of the variable domain as shown in figure 4, and the next change is called a multiplier factor function (Δ). This means that all parameters of each MF are a function of Δ, as shown in figure 5. Determination of the width and the centre point on each MF is expressed as the following equation:

Changes of the triangular center point are:

(11)

Triangular-wide changes are:

(12)

(13)

(14)

Where C, WR, and WL is the midpoint, wide right and wide left of the midpoint respectively, while the subscript "initial" means the initial value and the "new" is the new value after the change Δ. So, when the Δ value changes, the parameters of each MF will change include changes to the central triangle (C) and the width of the triangle (W) of the MF. The picture changes Δ is ​​shown in figure 6.

Value Δi (ΔER, ΔDE, ΔOT) consist of; ΔER as multiplicative factors to MF parameters of error input; ΔDE as multiplicative factors to MF parameters of delta error input; and ΔOT as multiplicative factors to MF parameters of output FLC.

The value of multiplier factor; ΔER, ΔDE, and ΔOT can be determined by trial and error, but in this paper, the value of multiplier factor is obtained through a learning process repeated until the optimal values are reached by using the PSO.

- Set of fuzzy rules consist of several fuzzy rules which are grouped into basic rules that are the basis of the decision making (inference process) to get action of the control signal output from a condition input. Thus, the total required rule base is 49 rules. Rule Base of FLC built is presented in Table 2.

- Defuzzification is the process of changing the fuzzy output variable back into a crisp variable.

Defuzzification method used in this paper is the Centroid defuzzification, which is a method of looking for a center of gravity (COG) of aggregate set, as shown in the following equation:

(15)

Proportional–Integral–Derivative (PID) Control

In the proposed control structure, there is a second control serving to refine the control systems. FLC output is used as the setting point of the yaw motion, so that the PID control works to eliminate the error among the set point of the yaw motion.

PID control is known as a system with superior control measures [17], including Proportional control (P) to speed up the system response rate (risetime), Integral control (I) to minimize or eliminate the steady-state error of the system and Derivative control (D) is to reduce the overshoot / undershoot. Performance control of P, I, and D is dependent on the determination of the constants Kp, Ki and Kd. In this paper, the value of the constants Kp, Ki and Kd is determined by the means of learning on the control system or tuning parameters to achieve the optimal composition of a constant value by using the PSO, the next three constants, are referred to as Kp = ΔKp, Ki = ΔKi and Kd = ΔKd. This is necessary because if ΔKp is too large, it will lead to instability of overshoot and even of the system. On the other hand, if the value of ΔKp is too small, it will reduce the precision adjustment and make the system in a static state so that the loss of dynamic characteristics happens. At constant values ​​of ΔKi, if it is too big, it will cause the response to overshoot, if ΔKi is too small, it is difficult to eliminate any steady-state error in the system, as well as to affect the accuracy of the system. Whereas if ΔKd is too large, it will slow down the response and the capability of the system will be reduced, as shown in figure 7.

Particle Swarm Optimization (PSO)

Optimization method based on swarm intelligence algorithm is called behaviorally inspired as an alternative to genetic algorithms, which is often called the evolution-based procedures [8]. This model is simulated in space with a certain dimension with a number of iterations so that at each iteration, the particle's position will increasingly lead to the intended target.

PSO is an optimization technique constructed by Dr.. Eberhart and Dr. Kennedy in 1995, inspired by social behavior of a flock of birds or fish [18]. Suppose that there is a flock of fish that are randomly looking for food on the region and there is only one food there. All of birds do not know where the food is, but they know how far they are from foods in each iteration. So the most effective strategy is to follow the fish closest to the food.

PSO is initialized with a population from random solutions and searches for the most optimal solution to update members of the population. Each random solution is called particle. Each particle moves in the problem space and has the best value that has been achieved, and this value is called pbest. The best other value is the best value achieved by any particle in the population, this value is called gbest. PSO has a velocity that would change the position from the particle at each iteration. At each iteration, the values of velocity and position are updated.

In this paper, optimization is done through the process of determining the position of the particle repeatedly to obtain the best position of the particle (convergent), this means that the particle has reached an optimal value. Particles are optimized as much as six variables: three variables are to determine the parameters of MF on the FLC, and the next three variables to determine the PID control parameters.

PSO algorithm consists of velocity and position [18], the basic equation is as follows, and velocity is:

(16)

and position is:

(17)

where :

i = index variable

j = index particle

k = iteration

v = velocity of the particle

Δ = position of the particle

P = the best position of the particle (pbest)

G = the best position of the swarm (gbest, best of all particle)

L1,2 = learning rates (social and cognitive constant)

R1,2 = random intervals [0 – 1]

W = inertia

Simulation, Results and Discussion

Simulation of active steering control of the vehicle is preceded by the process of optimization of the control system parameters using PSO. In this process, use control and optimization structure as shown in figure 3 were run using MATLAB SIMULINK. Vehicle models get steering input, in the form of look up table x - y trajectory as shown graphically in Figure 10, i.e. double lane change trajectory. Plant output is longitudinal motion (x) that always correlates with lateral motion (y) and yaw motion. Error lateral motion will be controlled by the FLC and yaw motion error will be controlled by PID control. Control parameters in FLC are parameters needed to determine the center and width of triangular MF i.e. ΔER, ΔDE, ΔOT and PID control parameters are constants to determine the gain of Kp, Ki and Kd, i.e. ΔKp, ΔKi, ΔKd. The six parameters will be optimized by PSO, so that the control system can work optimally. The optimization steps are as follows:

Step 1. Initialization parameters of PSO.

Optimization parameters of control systems using the PSO are as follows: the number of particles which is determined much as 30; maximum iteration which is set to 30; social and cognitive constant is which set equal to 1; inertia value which is determined to be 0.5; number of variables which is Δi = (ΔER ; ΔDE ; ΔOT ; ΔKp ; ΔKi ; ΔKd), and the vehicle parameters are shown in table 3.

Step 2. Initialization Swarm.

Initialization swarm consists of particles position and velocities initialization; where the inizialization is randomly made in i and j dimensions moving in the problem space. The particles position and velocities are expressed in the following equation:

(18)

; (i = 6 and j = 30) (19)

At the initial value is obtained;

the best local position (i, :) = particles position (i, :).

Step 3. Evaluation of population initialization.

Each particles was evaluated on the control system to get the fitness of each particles as shown in figure 3, a measure of fitness of the particles using the minimizing Integral of Time-weighted Absolute Error (ITAE) criterion [19]. Performance of the ITAE index is mathematically expressed as follows:

(20)

where t is the time and e(t) is error of the difference between reference/set point and controlled variable.

In this step, it will be obtained that

The best local fitness (i, :) = fitness of particles (i, :),

[The best global fitness, index] = min (The best local fitness (i, :)),

The best global position (i) = The best local position (i, index),

Furthermore, the best global position is acquired and updated using equations 16 and 17.

Step 5. Evaluation of New Particles.

At this stage, any new particles will be re-evaluated in the control system up to maximum number of iterations, as shown in figure 3, in each iteration, the particle positions are evaluated using the ITAE to obtain the fitness of particles. So,

If fitness of particles < The best local fitness,

then The best local fitness = fitness of particles,

and the best local position = particles position.

The best global fitness for each iteration kth should be obtained by;

[The best global fitness_particles (k), index] = min (The best local fitness),

If The best global fitness_particles (k) < The best global fitness,

then The best global fitness = The best global fitness_particles (k),

and The best global position (i) = The best local position (i, index).

In the next iteration, the best global position is updated again (using equations 16 and 17) until the maximum number of iterations is reached. Of the whole process over showed that the best global fitness has reached a convergence at iteration 5, as shown in figure 8. This means that, particle position corresponding to the index of the best global fitness is the particle position (Δi) which is optimal , the followings are the six optimal values acquired:

ΔER = 0.2923 ΔKp = 84.6357

ΔDE = 1.3776 ΔKi = 1.0095

ΔOT = 3.7602 ΔKd = 0.1923

ΔER , ΔDE and ΔOT are parameters that have been obtained which are a multiplying factor to determine the width of the triangle and the position of the center of each MF triangle of input and output FLC. These can be seen in table 4 and figure 9. Later, ΔKp, ΔKi and ΔKd that have been obtained are the value of the constants Kp, Ki and Kd that will determine the performance of the Proportional, Integral and Derivative controls.

the parameter expressions for Proportional, Integral and Derivative controls.

PSO performs optimization until the maximum iteration reaches 30 iterations on the control structure of the model of automatic steering vehicle with plant input look up table (x - y trajectory) at a constant speed of 13.88 m/s. This means that the control system has made the learning process with random parameters, and at the end it was able to get the values ​​of the optimal parameters such that the value of lateral motion has the smallest error. The measure of error used in the optimization process is ITAE, which at the time reached the convergence at fifth iteration, where ITAE value is 1.3467 e-54 and this value corresponds to the value of Continues Root Mean Square Error (C-RMS error) of 0.005689.

Furthermore, the six parameters obtained from the optimization process are defined as a parameter of the system control (called FLC-PID tuned PSO) to the model automatic steering control of vehicle. The simulation of vehicle steering control system is done ​​with two different kinds of input look up table (x - y trajectory): Double Lane Change and Sinewave with speeds varying from 10-100 km / h. The performance of the simulation is also compared against the model of automatic steering control of vehicle control system without optimization (called PID-PID and FLC-PID) as shown in Table 5.

In the simulation results, it is found that with the use of FLC system on the lateral motion and the PID control system in the yaw motion tuned with PSO (FLC-PID tuned PSO), the vehicle motion is always able to be maintained according to the desired trajectory with a smaller error and limits higher speed than by using FLC system and PID control systems without the tuned (FLC-PID) and the PID-PID control system as shown in Table 5. Since the performance of the Main control system is that performance of the lateral motion that is affected by 9 out of 10 DOF as intended, in this paper they are shown only input, output and error on lateral motion. Figures 10 and 11 show the graphs between the input and output of the simulation for the Double Lane Change and Sinewave Trajectory respectively, figures 12 and 13 show the error lateral motion of Double Lane Change and Sinewave Trajectory, respectively.

Simulation that has been done above shows that the control system can replaced with the desired control system to be compared on the error and speed that can be achieved, although the best results have not shown the best results on the test hardware. The simulation described in this paper is a recommendation that further research be conducted in the form of testing Hardware In the Loop simulations (HILS).

Conclusion

This paper represents a method of optimizing the use of Particle Swarm Optimization (PSO) to determine the parameters of the optimal control system, the control system used is a cascade control system; FLC as a lateral motion control system and PID control as the yaw motion control system, are applied to the simulation of automatic steering control of the vehicle models with 10-DOF, simulation is performed with two kinds of input x - y desired trajectory, the Double Lane Change and Sine steer trajectory, the results obtained are vehicle motion that can be maintained in accordance with the desired trajectory with a smaller error and can reach higher speeds than with the control system that uses non-optimized parameters.

Refferences

[1] Avak B. Modeling and Control of a Superimposed Steering System. MSc, School of Electrical and Computer Engineering Georgia Institute of Technology, Georgia, 2004.

[2] Park Y, Jung I, Semi-Active Steering Wheel for Steer-By-Wire System, SAE International, Warrendale, PA, 2001;01-3306.

[3] Hingwe P, Tan HS, Packard AK, Tomizuka M. Linear parameter varying controller for automated lane guidance: experimental study on tractor-trailers. IEEE Transactions on Control Systems Technology 2002; 10: 793 – 806.

[4] Hernandez JI, Kuo CY. Steering control of automated vehicles using absolute positioning GPS and magnetic markers. IEEE Transactions on Vehicular Technology 2003; 52: 150 – 161.

[5] Hernandez JI, Kuo CY. Lateral control of higher order nonlinear vehicle model in emergency maneuvers using absolute positioning GPS and magnetic markers. IEEE Transactions on Vehicular Technology 2004; 53: 372 – 384.

[6] Cai L, Rad AB, Chan WL. A Genetic Fuzzy Controller for Vehicle Automatic Steering Control. IEEE Transactions on Vehicular Technology 2007; 56: 529 –543.

[7] Ping EP, Hudha K, Jamaluddin H. Hardware-in-the-loop simulation of automatic steering control for lanekeeping manoeuvre: outer-loop and inner-loop control design. International Journal of Vehicle Safety 2010; 5: 35–59.

[8] Amin SHM, Adriansyah A. Particle Swarm Fuzzy Controller for Behavior-based Mobile Robot. presented at the 9th International Conference on Control, Automation, Robotics and Vision, ICARCV ’06; 5-8 December 2006; Singapore: IEEE. pp. 1–6.

[9] Wei S. Liu M, Song Y. The Optimizing of Fuzzy Control Rule Based on Particle Swarm Optimization Algorithms. in Proceedings of the 2009 Third International Conference on Genetic and Evolutionary Computing; 14-17 October 2009; Washington, DC, USA: IEEE. pp. 645–648.

[10] Hudha K, Kadir ZA, Said MR, Jamaluddin H. Modelling, validation and roll moment rejection control of pneumatically actuated active roll control for improving vehicle lateral dynamics performance. International Journal of Engineering Systems Modelling and Simulation 2009; 1: 122.

[11] Ahmad F, Hudha K, Jamaluddin H. Gain Scheduling PID Control with Pitch Moment Rejection for Reducing Vehicle Dive and Squat. International Journal of Vehicle Safety 2009; 4: 1–30.

[12] Falcone P, Borrelli F, Asgari J, Tseng HE, Hrovat D. Predictive Active Steering Control for Autonomous Vehicle Systems. IEEE Transactions on Control Systems Technology 2007; 15: 566 –580.

[13] Stone MR, Demetriou MA. Modeling and simulation of vehicle ride and handling performance. presented at the Proceedings of the 2000 IEEE International Symposium on Intelligent Control; 19-19 July 2000, Rio Patras: IEEE. pp. 85 –90.

[14] Wang J, Hsieh MF. Vehicle yaw inertia and mass independent adaptive control for stability and trajectory tracking enhancements. in American Control Conference. ACC ’09; ; 10-12 June 2009; St. Louis, MO: IEEE. pp. 689 –694.

[15] Fachrudin, Robandi I, Sutantra N. Model and Simulation of Vehicle Lateral Stability Control. presented at the 2nd APTECS, 2010, International Seminar on Applied Technology, Science, and Arts; 21–22 December 2010; Surabaya, ITS: p. 26.

[16] Obaid ZA, Sulaiman N, Marhaban MH, Hamidon MN. Analysis and Performance Evaluation of PD-like Fuzzy Logic Controller Design Based on Matlab and FPGA. IAENG International Journal of Computer Science 2010; 37: 146 -156.

[17] Xiuwei F, Li F, Feng K. Research of Automotive Steer-by-Wire Control Based on Integral Partition PID Control. presented at 3rd International Conference on Genetic and Evolutionary Computing, WGEC '09, 14-17 October 2009; China: IEEE. 561-564.

[18] Kennedy J, Eberhart R. Particle swarm optimization. presented at the IEEE International Conference on Neural Networks, Proceedings; 27 Nov- 1 Dec 1995; University of Western Australia, Perth, Western Australia: IEEE. pp. 1942 –1948.

[19] Martins FG. Tuning PID Controllers using the ITAE Criterion. The International Journal of Engineering Education 2005; 21: 867-873.

mufr

Ksfrr

Csfrr

Zufrr

Zrfrr

Ktfrr

Zsrrr

Zsrlr

Zsfrr

Zsfl

mufl

Ksfl

Csfl

Zufl

Zrfl

Ktfl

mufr

Ksrr

Csrr

Zurr

Zrrr

Ktrr

murl

Ksrl

Csrl

Zurl

Zrrl

Ktrl

z

x

y

φφ

z

θ

Figure 1. Vehicle Ride Model

Mzrl

Fxrl

Fxrl

Mzrl

Fxrl

Fxrl

Mzrl

Fxrl

Fxrl

δ

Mzrl

Fxrl

Fxrl

δ

vy

vx

β

r

CG

lr

lf

w

Figure 2. Vehicle Handling Model

Figure 3. The Control and Optimization Structure for active steering control on vehicle model

ΔER, ΔDE, ΔOT

Particle Swarm Optimization

The best value of

ΔER, ΔDE, ΔOT, ΔKp, ΔKi, ΔKd

PID

+

-

+

-

du/dt

x

Steering y

Input

yaw

x

y

yaw

Look up table

x – y Trajectory

Error y

Error yaw

ITAE

Criteria

FLC Control

PID Control

Inisialisasi:

Random of Particle Position

(ΔER, ΔDE, ΔOT, Kp, Ki, Kd)

ΔKp, ΔKi, ΔKd

Vehicle Model

-2.5Δ -2Δ -1.5Δ -1Δ -0.5Δ 0 0.5Δ 1Δ 1.5Δ 2Δ 2.5Δ

NB NS NK Z PK PS PB

Figure 5. Parameter Membership Function

Degree of

membership (

1

0

Domain (x)

WRn

Figure 4. Parameter Membership Function

Degree of

membership (

1

0

Domain (x)

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5

-1 -0.5 0 0.5 1

-4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4

-5 -4.5 -4 -3.5- -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5

Figure 6. Change the width and center of the membership function

Degree of

membership (

Domain (x)

Domain (x)

Domain (x)

Domain (x)

NB NS NK Z PK PS PB

NB NS NK Z PK PS PB

NB NS NK Z PK PS PB

NB NS NK Z PK PS PB

Δ = 2

Δ = 1.5

Δ = 1

Δ = 0.5

∑

Plant

Set point

Output

Error

+ _

Figure 7. PID Control

Figure 8. Convergence of PSO Algorithm Graphic

Figure 9. Membership Function of FLC

D:\My Study\Steer by wire\Publication Record on Phd Student\Jurnal turkey\fig DLC PSO.PNG

Figure 10. Input and Output Lateral Motion for Double Lane Change Trajectory

Figure 12. Error Lateral Motion for Double Lane Change Trajectory

Figure 11. Input and Output Lateral Motion for Sinewave Trajectory

Figure 13. Error Lateral Motion for Sinewave Trajectory

TABLE 1

DEFINITIONS OF VARIABLES

Variabel

Definitions

sprung mass displacement at body CoG

sprung mass velocity at body CoG

sprung mass acceleration at body CoG

unsprung masses displacement

unsprung masses velocity

unsprung masses acceleration

road profiles at each tyres

suspension spring stiffness each tyres

suspension damping each tyres

roll axis moment of inertia

pitch axis moment of inertia

wheel base of sprung mass

suspension force each corner

sprung mass weight

unsprung mass weight

total vehicle mass

self-aligning moments

pneumatic actuator forces at each corner

tire forces in longitudinal direction

tire forces in lateral direction

indicating front or rear

indicating left or right

moment of inertia around the z-axis

steering angle

distance between front of vehicle and CoG.

distance between rear of vehicle and CoG.

pitch angle at body centre of gravity

pitch rate at body centre of gravity

roll acceleration at body centre of gravity

roll angle at body centre of gravity

roll rate at body centre of gravity

roll acceleration at body centre of gravity

Table 2. Rule Base of Fuzzy Logic Controller

Delta

error

Error

NB

NS

NK

Z

PK

PS

PB

NB

NB

NB

NB

NB

NS

NK

Z

NS

NB

NB

NB

NS

NK

Z

PK

NK

NB

NB

NS

NK

Z

PK

PS

Z

NB

NS

NK

Z

PK

PS

PB

PK

NS

NK

Z

PK

PS

PB

PB

PS

NK

Z

PK

PS

PB

PB

PB

PB

Z

PK

PS

PB

PB

PB

PB

Table 3 Vehicle model simulation parameters

No

Parameter

Value

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

Vehicle mass

Vehicle sprung mass

Coefficient of friction

Front track width

Rear track width

Tyre rolling radius

Wheelbase

Distance between front axle to COG

Distance between rear axle to COG

Pitch stiffness constant

Roll stiffness constant

Centre of gravity height

Pitch moment of inertia

Roll moment of inertia

Yaw moment of inertia

Wheel moment of inertia

Pitch damping constant

Roll damping constant

1700 kg

1520 kg

0.85

1.5 m

1.5 m

0.285 m

2.7 m

1.11 m

1.59 m

4000 Nm-1

2400 Nm-1

0.55 m

425 kg m2

425 kg m2

3125 kg m2

1.1 kg m2

170000 Nm-1s-1

90000 Nm-1s-1

Table 4. Result of centre and width of MF triangle

ERROR INPUT

ΔER = 0.2923

Width Left

Centre

Width Right

NB

-0.73075

-0.43845

-0.14615

NK

-0.5846

-0.2923

0

NS

-0.43845

-0.14615

0.14615

Z

-0.2923

0

0.2923

PK

-0.14615

0.14615

0.43845

PS

0

0.2923

0.5846

PB

0.14615

0.43845

0.73075

DELTA ERROR INPUT

ΔDE = 1.3776

Width Left

Centre

Width Right

NB

-3.444

-2.0664

-0.6888

NK

-2.7552

-1.3776

0

NS

-2.0664

-0.6888

0.6888

Z

-1.3776

0

1.3776

PK

-0.6888

0.6888

2.0664

PS

0

1.3776

2.7552

PB

0.6888

2.0664

3.444

OUTPUT

ΔOT = 3.7602

Width Left

Centre

Width Right

NB

-9.4005

-5.6403

-1.8801

NK

-7.5204

-3.7602

0

NS

-5.6403

-1.8801

1.8801

Z

-3.7602

0

3.7602

PK

-1.8801

1.8801

5.6403

PS

0

3.7602

7.5204

PB

1.8801

5.6403

9.4005

Table 5. Benchmark Control System

No

Velocity

C-RMS Error

Double Lane Change

Km/h

m/s

PID – PID

FLC – PID

FLC – PID

tuned PSO

1

10

2.77

0.30970

0.104200

0.043310

2

20

5.55

0.64640

0.033450

0.023370

3

30

8.33

0.02211

0.017260

0.011490

4

40

11.11

0.01743

0.011800

0.007558

5

50

13.89

0.01096

0.009131

0.005625

6

60

16.67

0.01008

0.008129

0.004647

7

70

19.45

time out

0.007949

0.004864

8

80

22.22

time out

0.010050

0.005111

9

90

24.99

time out

time out

0.006101

10

100

27.77

time out

time out

time out

11

110

30.55

time out

time out

time out

No

Velocity

C-RMS Error

Sinewave

Km/h

m/s

PID – PID

FLC – PID

FLC – PID

tuned PSO

1

10

2.77

divergen

0.029190

0.0188500

2

20

5.55

0.010640

0.008328

0.0049970

3

30

8.33

0.005704

0.004325

0.0024990

4

40

11.11

0.004244

0.002852

0.0016250

5

50

13.89

0.003741

0.002174

0.0012240

6

60

16.67

0.003444

0.001851

0.0010010

7

70

19.45

0.003128

0.001808

0.0009329

8

80

22.22

divergen

0.002134

0.0008786

9

90

24.99

divergen

0.007718

0.0009079

10

100

27.77

divergen

divergen

0.0009911

11

110

30.55

divergen

divergen

0.0011870